Prove for the following statement using course resources such as our notes and textbooks. Your proof should be your own work, so you should not use any other resources. Record a short presentation or create a slideshow explaining your proof. Make sure that you clearly state any definitions, axioms, or theorems that you are using.

Suppose R is a non-square rhombus.

  1. List the symmetries of R. Write as a composition of translations, reflections, and rotations.

  2. Prove that the set of symmetries of R is a group under composition.